ODE
\[ y(x) y'(x)+x=0 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.00544579 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\sqrt {2 c_1-x^2}\right \},\left \{y(x)\to \sqrt {2 c_1-x^2}\right \}\right \}\]
Maple ✓
cpu = 0.004 (sec), leaf count = 14
\[ \left \{ {x}^{2}+ \left ( y \left ( x \right ) \right ) ^{2}-{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[x + y[x]*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> -Sqrt[-x^2 + 2*C[1]]}, {y[x] -> Sqrt[-x^2 + 2*C[1]]}}
Maple raw input
dsolve(y(x)*diff(y(x),x)+x = 0, y(x),'implicit')
Maple raw output
x^2+y(x)^2-_C1 = 0